Tunable single-photon frequency converter in a waveguide with a giant V-type atom

TL;DR

This work analyzes single-photon scattering in a 1D waveguide coupled to a V-type giant atom with a driven transition, using the Lippmann-Schwinger formalism to derive exact scattering amplitudes. The two spatially separated GA-waveguide couplings create nonlocal interference, enabling elastically and inelastically scattered photons to exchange frequency by the GA’s dressed-state splitting, with the conversion controlled by phase differences and the Markovian vs non-Markovian regime. A key result is that conversion efficiency is bounded by 1/2 under reciprocity, but nonreciprocity induced by the coupling-phase difference can boost the conversion probability to unity, especially in the non-Markovian regime where multiple spectral features emerge and bound-state in continuum effects appear. These insights provide a pathway for efficient, tunable single-photon frequency conversion in conventional waveguides, with potential applications in quantum networks and interfacing heterogeneous nodes.

Abstract

We study the single-photon scattering in a one-dimensional (1D) waveguide coupled to one transition of a $V$-type giant atom (GA), whose other transition is coherently driven by an classical field. The inelastic scattering of single photons by the GA realizes the single-photon frequency conversion. By applying the Lippmann-Schwinger equation, the scattering coefficients for single photons incident from different directions are obtained, which present different scattering spectra in the Markovian and the non-Markovian regimes. The conversion contrast characterizing the nonreciprocity is also analyzed in both regimes. It is found that the probability of the frequency up- or down-conversion vanishes as long as the emission from either transition pathways for single photons is suppressed, but it is enhanced and even reach unity by introducing the nonreciprocity. It is the quantum self-interference induced by the scale of this two-legged GA and the phase difference between the GA-waveguide couplings that tune the probability of the frequency up- or down-conversion.

Figures (6)

• Figure 1: Schematic of frequency conversion using a three-level GA with a V-type configuration coupled to a linear waveguide. The transition $|e\rangle \leftrightarrow |g\rangle$ is coupled to the waveguide at positions $x=-d/2$ and $x=d/2$, and transition $|g\rangle \leftrightarrow |f\rangle$ is driven by a classical field with frequency $\omega _{d}$ and Rabi frequency $\Omega$.
• Figure 2: (a), (d)/(g) transmittance $T$, (b), (e)/(h) reflectance $R$, and (c), and (f)/(i) conversion probability $T_c$ versus detuning coefficient $\Delta_{k}^{-}/\Gamma$ and phase delay coefficient $(\phi_{+}/\pi)$/$(\phi_{-}/\pi)$ for (a)-(c) $\varphi_J=\pi, \phi_{-}=0.75\pi$, (d)-(f) $\varphi_J=0.75\pi, \phi_{-}=\pi$, and (g)-(i) $\varphi_J=\pi, \phi_{+}=\pi/3$. The dashed and dash-dotted lines in (b) and (e) represent the position for maximum reflection, respectively. The dash-dotted line in (g) represents the position for total transmission. We have set $|J_1|=|J_2|$ and $\theta=\pi/2$ in all panels.
• Figure 3: The conversion probability $T_c$ versus detuning $\Delta_{k}^{-}/\Gamma$ for given $\phi_{\pm},\varphi_J$. We have set $|J_1|=|J_2|$ and $\theta=\pi/2$ in all panels.
• Figure 4: The conversion contrast $I_2$ versus detuning $\Delta_{k}^{-}/\Gamma$ and $\phi_{+}$ for (a) $\varphi_{J}=0.1\pi, \phi_{-}=1.1\pi$, (b)$\varphi_{J}=0.3\pi, \phi_{-}=1.3\pi$, (c) $\varphi_{J}=0.5\pi, \phi_{-}=1.5\pi$. (d) The conversion contrast for different $\phi_{-}$ when $\varphi_{J}=\pi/2$. We have set $|J_1|=|J_2|$ and $\theta=\pi/2$.
• Figure 5: (a, b)The transmittance $T=\tilde{T}$ (dashed red curve), reflectance $R=\tilde{R}$ (solid blue curve) and the conversion probability $T_c=\tilde{T}_c$ (dotted-dash green curve) versus detuning $\Delta_{k}^{-}/\Gamma$ when $\varphi_{J}=(2n+1)\pi$, (a) $\tau\Gamma=1.0025\pi$ and (b) $\tau\Gamma=0.9975\pi$. We have set $|J_1|=|J_2|$, $\theta=\pi/2$, $\omega_e=600\Gamma$, $\Omega=1.5\Gamma$. (c, d) The conversion probability $T_c$ versus detuning $\Delta_{k}^{-}$ for given $\phi_{\mp}$ and $\varphi_{J}=(2n+1)\pi$.